dolphin
Get Started

SAT Math skill page

SAT Quadratic Equations Practice

Handle SAT quadratic questions by recognizing roots, factors, parabolas, and the meaning of each solution.

Practice quadratic equations in Dolphin Try examples
14-20 min practice time 3 examples on page Advanced Math
Practice time 14-20 min
On-page examples 3 examples
Best for Advanced Math

What this tests

What to know for this SAT skill

Practice examples

Try a few SAT-style questions

Example 1 Easy

If x is positive and x^2 = 49, what is x?

  1. -7
  2. 0
  3. 7
  4. 49
Show answer and explanation

Answer: 7

The solutions to x^2 = 49 are x = 7 and x = -7. Since x is positive, x = 7.

Example 2 Medium

If x^2 - 5x + 6 = 0, what is the sum of the two solutions?

  1. 2
  2. 3
  3. 5
  4. 6
Show answer and explanation

Answer: 5

Factor the equation as (x - 2)(x - 3) = 0, so the solutions are 2 and 3. Their sum is 5.

Example 3 Hard

The height h, in feet, of a ball t seconds after launch is h = -16t^2 + 64t. After how many seconds does the ball return to the ground?

  1. 2
  2. 3
  3. 4
  4. 8
Show answer and explanation

Answer: 4

Set h = 0: -16t^2 + 64t = 0. Factor to get -16t(t - 4) = 0, so t = 0 or t = 4. The return time after launch is 4 seconds.

Avoid these traps

Common mistakes on this skill

Forgetting the second solution

Quadratics can have two roots. Check whether the problem wants one root, both roots, or a contextual answer.

Dropping a negative sign

Factoring and expanding quadratics often hinge on signs. Test your factors by multiplying them back out.

Using a context-impossible root

In word problems, a negative time or length may be algebraically valid but not meaningful.

Study plan

How to practice this skill in Dolphin

  1. Memorize the factor patterns for simple trinomials.
  2. Practice setting each factor equal to zero after factoring.
  3. Connect roots to x-intercepts on a graph.
  4. For word problems, reject roots that do not make sense in context.
Practice quadratic equations in Dolphin

Related practice

Build the surrounding skills

SAT Linear Functions PracticeSAT Linear Equations PracticeSAT Geometry PracticeSAT Math skill hub

Skill cluster

Keep practicing SAT Math

SAT Math skill hub SAT Linear Equations PracticeSAT Systems of Equations PracticeSAT Linear Functions PracticeSAT Percentages PracticeSAT Ratios and Proportions PracticeSAT Probability PracticeSAT Geometry PracticeSAT Right Triangles PracticeSAT Data Analysis PracticeSAT Circle Equations Practice SAT Reading and Writing Practice Pages Dolphin SAT study guides SAT score guides by college

FAQ

Questions about SAT Quadratic Equations Practice

Do I need the quadratic formula for the SAT?

It can help, but many SAT quadratic questions are designed for factoring, graph interpretation, or simple structure recognition.

What is a root of a quadratic?

A root is an x-value that makes the quadratic equal zero. On a graph, roots are x-intercepts.

Why are quadratic word problems tricky?

They often produce more than one algebraic solution, and you have to decide which one fits the situation.